What is the limit as x approaches 1+of (1-sqrt(x))/(sqrt(x)(x-1)) ?

The limit as x approaches 1+of (1-sqrt(x))/(sqrt(x)(x-1)) is -1/2

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limit as x approaches 1+of (1-sqrt(x))/(sqrt(x)(x-1))

x \to 1 + lim (\frac{1 - x}{x ( x - 1 )})

- \frac{1}{2}

Decimal

- 0.5

Solution steps

x \to 1 + lim (\frac{1 - x}{x ( x - 1 )})

Multiply by the conjugate of

1 - x : \frac{1 - x}{1 + x}

= x \to 1 + lim (\frac{\frac{1 - x}{1 + x}}{x ( x - 1 )})

Simplify

\frac{\frac{1 - x}{1 + x}}{x ( x - 1 )} : - \frac{1}{x ( x + 1 )}

= x \to 1 + lim (- \frac{1}{x ( x + 1 )})

Plug in the value

x = 1

= - \frac{1}{1 ( 1 + 1 )}

Simplify

= - \frac{1}{2}

\frac{d}{d x} (cos^{2} (3 π x))

x \to - 9 - lim (\frac{x + 8}{x + 9})

\int \frac{( x ^{2} + 1 )}{x ( x - 1 ) ^{3}} d x

\int sec (x) \frac{1}{x} d x

\frac{d}{d x} (\frac{x}{5} - \frac{5}{x})

What is the limit as x approaches 1+of (1-sqrt(x))/(sqrt(x)(x-1)) ?
The limit as x approaches 1+of (1-sqrt(x))/(sqrt(x)(x-1)) is -1/2